JEE Exam > JEE Questions > An electron of mass m when accelerated throug...
Start Learning for Free
An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will be
- a)λ m/M
- b)λ √m/M
- c)λ M/m
- d)λ √M/m
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
An electron of mass m when accelerated through a potential difference ...
Explanation:
This problem can be solved using the de Broglie wavelength formula:
\[\lambda = \frac{h}{\sqrt{2mE}}\]
where h is the Planck constant, m is the mass of the particle, and E is the energy of the particle.
Given:
- For an electron: \[\lambda_{e} = \frac{h}{\sqrt{2m_{e}eV}}\]
- For a proton: \[\lambda_{p} = \frac{h}{\sqrt{2m_{p}eV}}\]
where m_e is the mass of the electron, m_p is the mass of the proton, V is the potential difference, and e is the charge of an electron.
Comparing the two wavelengths:
\[\frac{\lambda_{p}}{\lambda_{e}} = \frac{\sqrt{m_{e}}}{\sqrt{m_{p}}}\]
\[\lambda_{p} = \lambda_{e} \times \frac{\sqrt{m_{e}}}{\sqrt{m_{p}}}\]
Therefore, the de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will be \[\lambda = \lambda_{e} \times \frac{\sqrt{m_{e}}}{\sqrt{m_{p}}}\]
This can be simplified as \[\lambda = \lambda_{e} \times \sqrt{\frac{m_{e}}{m_{p}}}\]
Hence, the correct answer is option B: \[\lambda = \lambda_{e} \times \sqrt{\frac{m_{e}}{m_{p}}}\]
This problem can be solved using the de Broglie wavelength formula:
\[\lambda = \frac{h}{\sqrt{2mE}}\]
where h is the Planck constant, m is the mass of the particle, and E is the energy of the particle.
Given:
- For an electron: \[\lambda_{e} = \frac{h}{\sqrt{2m_{e}eV}}\]
- For a proton: \[\lambda_{p} = \frac{h}{\sqrt{2m_{p}eV}}\]
where m_e is the mass of the electron, m_p is the mass of the proton, V is the potential difference, and e is the charge of an electron.
Comparing the two wavelengths:
\[\frac{\lambda_{p}}{\lambda_{e}} = \frac{\sqrt{m_{e}}}{\sqrt{m_{p}}}\]
\[\lambda_{p} = \lambda_{e} \times \frac{\sqrt{m_{e}}}{\sqrt{m_{p}}}\]
Therefore, the de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will be \[\lambda = \lambda_{e} \times \frac{\sqrt{m_{e}}}{\sqrt{m_{p}}}\]
This can be simplified as \[\lambda = \lambda_{e} \times \sqrt{\frac{m_{e}}{m_{p}}}\]
Hence, the correct answer is option B: \[\lambda = \lambda_{e} \times \sqrt{\frac{m_{e}}{m_{p}}}\]
Free Test
FREE
| Start Free Test |
Community Answer
An electron of mass m when accelerated through a potential difference ...
Explanation:
Given:
- Mass of electron (m) accelerated through a potential difference V has de Broglie wavelength λ.
- Mass of proton (M) accelerated through the same potential difference V is to be determined.
De Broglie wavelength formula:
λ = h / p
where h is the Planck's constant and p is the momentum of the particle.
Relation between momentum and potential difference:
For an accelerated particle, momentum can be related to the potential difference by the equation:
p = √(2mV)
De Broglie wavelength for electron:
Substitute the momentum of the electron in the de Broglie wavelength formula:
λ = h / √(2mV)
De Broglie wavelength for proton:
Now, for the proton accelerated through the same potential difference V:
p = √(2MV)
Substitute the momentum of the proton in the de Broglie wavelength formula:
λ' = h / √(2MV)
Comparing the wavelengths:
To compare the wavelengths of the electron and proton:
λ' / λ = (h / √(2MV)) / (h / √(2mV))
λ' / λ = √(m / M)
Therefore, the de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will be:
λ' = λ √(m / M) (Option 'B')
Given:
- Mass of electron (m) accelerated through a potential difference V has de Broglie wavelength λ.
- Mass of proton (M) accelerated through the same potential difference V is to be determined.
De Broglie wavelength formula:
λ = h / p
where h is the Planck's constant and p is the momentum of the particle.
Relation between momentum and potential difference:
For an accelerated particle, momentum can be related to the potential difference by the equation:
p = √(2mV)
De Broglie wavelength for electron:
Substitute the momentum of the electron in the de Broglie wavelength formula:
λ = h / √(2mV)
De Broglie wavelength for proton:
Now, for the proton accelerated through the same potential difference V:
p = √(2MV)
Substitute the momentum of the proton in the de Broglie wavelength formula:
λ' = h / √(2MV)
Comparing the wavelengths:
To compare the wavelengths of the electron and proton:
λ' / λ = (h / √(2MV)) / (h / √(2mV))
λ' / λ = √(m / M)
Therefore, the de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will be:
λ' = λ √(m / M) (Option 'B')
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer?
Question Description
An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer?.
An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer?.
Solutions for An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An electron of mass m when accelerated through a potential difference V has de Broglie wavelength λ. The de Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will bea)λ m/Mb)λ √m/Mc)λ M/md)λ √M/mCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup